Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (m²), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.

Ruins are the remains of human-made architecture: structures that were once complete, as time went by, have fallen into a state of partial or complete disrepair, due to lack of maintenance or deliberate acts of destruction. Natural disaster, war and depopulation are the most common root causes, with many structures becoming progressively derelict over time due to long-term weathering and scavenging.

There are famous ruins all over the world, from ancient sites in China, the Indus valley and Judea to Zimbabwe in Africa, ancient Greek, Egyptian and Roman sites in the Mediterranean basin, and Incan and Mayan sites in the Americas. Ruins are of great importance to historians, archaeologists and anthropologists, whether they were once individual fortifications, places of worship, houses and utility buildings, or entire villages, towns and cities. Many ruins have become UNESCO World Heritage Sites in recent years, to identify and preserve them as areas of outstanding value to humanity.

Ancient cities were often highly militarized and fortified defensive settlements. In times of war they were the central focus of armed conflict and would be sacked and ruined in defeat. Although less central to modern conflict, vast areas of 20th century cities such as Warsaw, Dresden, Coventry, London and Berlin were left in ruins following World War II, and a number of major cities around the world – such as Beirut, Kabul, Sarajevo, Grozny and Baghdad – have been partially or completely ruined in recent years as a result of more localised warfare.

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